1. Richard B. Rood (Room 2525, SRB)
AOSS 401 Geophysical Fluid Dynamics: Atmospheric Dynamics Prepared: Thermal Wind / Vertical Wind / Thermal Circulation
Richard B. Rood (Room 2525, SRB)
Cell:

2. Class News Ctools site (AOSS 401 001 F13)
Second Examination on December 10, 2013
Homework
Watch for Ctools /

3. Weather National Weather Service Weather Underground
Model forecasts:
Weather Underground
NCAR Research Applications Program

4. Outline Thermal wind Revisit the Tour of the Earth Vertical wind
Vertical structure
Vertical wind
Formation of a circulation feature

5. Approximated equations of motion in pressure coordinates

6. Geostrophic wind

7. Hydrostatic Balance

8. Schematic of thermal wind.
Thickness of layers related to temperature. Causing a tilt of the pressure surfaces.
from Brad Muller

9. What is a tactic for exploring vertical behavior?

10. Geostrophic wind Take derivative wrt p.
Links horizontal temperature gradient
with vertical wind gradient.

11. Thermal wind
p is an independent variable, a coordinate. Hence, x and y derivatives are taken with p constant.

12. A excursion to the atmosphere. Zonal mean temperature - Jan
approximate tropopause
south (summer)
north (winter)

13. A excursion to the atmosphere. Zonal mean temperature - Jan
∂T/∂y ?
south (summer)
north (winter)

14. A excursion to the atmosphere. Zonal mean temperature - Jan
∂T/∂y ?
south (summer)
north (winter)

15. A excursion to the atmosphere. Zonal mean temperature - Jan
∂T/∂y ?
<0
<0
<0
<0
>0
<0
south (summer)
north (winter)

16. A excursion to the atmosphere. Zonal mean temperature - Jan
∂T/∂y ?
∂ug/∂p ?
<0
>0
<0
<0
>0
<0
<0
<0
> 0
>0
>0
<0
south (summer)
north (winter)

17. A excursion to the atmosphere. Zonal mean wind - Jan
south (summer)
north (winter)

18. Relation between zonal mean temperature and wind is strong
This is a good diagnostic – an excellent check of consistency of temperature and winds observations.
We see the presence of jet streams in the east-west direction, which are persistent on seasonal time scales.
Is this true in the tropics?

19. Thermal wind

20. Thermal wind

21. Thermal wind

22. Thermal wind ?

23. From Previous Lecture Thickness
Note link of thermodynamic variables, and similarity to scale heights calculated in idealized atmospheres
Z2-Z1 = ZT ≡ Thickness - is proportional to temperature is often used in weather forecasting to determine, for instance, the rain-snow transition.

24. Similarity of the equations
There is a direct relationship between thermal wind and thickness.

25. Schematic of thermal wind.
Thickness of layers related to temperature. Causing a tilt of the pressure surfaces.
from Brad Muller

26. In class problems Group A Group B Scott Anna Alex James Justin Kevin
John
Ross
Rachel
Trent
Jordan

27. Another excursion into the atmosphere.
850 hPa surface
300 hPa surface
Identify: Surface low and trough / Upper troposphere low and trough
Using state boundaries: describe position or surface and upper trop features
Describe surface temperature advection
from Brad Muller

28. Another excursion into the atmosphere.
850 hPa surface
300 hPa surface

29. Another excursion into the atmosphere.
850 hPa surface
300 hPa surface

30. Another excursion into the atmosphere.
850 hPa surface
300 hPa surface

31. Another excursion into the atmosphere.
850 hPa surface
300 hPa surface

32. A summary of ideas.
In general, these large-scale, middle latitude dynamical features tilt westward with height.
The way the wind changes direction with altitude is related to the advection of temperature, warming or cooling in the atmosphere below a level.
This is related to the growth and decay of these disturbances.
Lifting and sinking of geopotential surfaces.

33. Schematic of thermal wind.
Thickness of layers related to temperature. Causing a tilt of the pressure surfaces.
from Brad Muller

34. Outline
Vertical Motion
Rotation in Fluid, Vorticity

35. Vertical motions: The relationship between w and 
= 0
hydrostatic equation
≈ 1m/s 1Pa/km ≈ 1 hPa/d
≈ 100 hPa/d
≈ 10 hPa/d

36. Link between  and the ageostrophic wind
= 0
Links the horizontal and vertical motions. Since geostrophy is such a good balance, the vertical motion is linked to the divergence of the ageostrophic wind (small).

37. Vertical pressure velocity : Kinematic method
For synoptic-scale (large-scale) motions in midlatitudes the horizontal velocity is nearly in geostrophic balance. Recall: the geostrophic wind is nondivergent (for constant Coriolis parameter), that is Horizontal divergence is mainly due to small departures from geostrophic balance (ageostrophic wind).
Therefore: small errors in evaluating the winds <u> and <v>
lead to large errors in . The kinematic method is inaccurate.

38. Think about this ... If I have errors in data, noise.
What happens if you average that data?
What happens if you take an integral over the data?
What happens if you take derivatives of the data?

39. Estimating the vertical velocity: Adiabatic Method
Start from thermodynamic equation in p-coordinates:
Assume that the diabatic heating term J is small (J=0), re-arrange the equation
- (Horizontal temperature advection term)
Sp:Stability parameter

40. Estimating the vertical velocity: Adiabatic Method
Horizontal temperature advection term
Stability parameter
If T/t = 0 (steady state), J=0 (adiabatic) and Sp > 0 (stable):
then warm air advection:  < 0, w ≈ -/g > 0 (ascending air)
then cold air advection:  > 0, w ≈ -/g < 0 (descending air)

41. Adiabatic Method
Based on temperature advection, which is dominated by the geostrophic wind, which is large. Hence this is a reasonable way to estimate local vertical velocity when advection is strong.

42. Estimating the vertical velocity: Diabatic Method
Start from thermodynamic equation in p-coordinates:
If you take an average over space and time, then the advection and time derivatives tend to cancel out.
Diabatic term

43. An example that connects it all

44. Equations of motion in pressure coordinates (plus hydrostatic and equation of state)

45. Let’s think about growing and decaying disturbances.
Mass continuity equation.

46. Let’s think about growing and decaying disturbances.
Formally links vertical wind and divergence.

47. Remember
What is the definition of omega, ω?

48. Let’s think about growing and decaying disturbances.
Convergence (divergence) of mass into (from) column above the surface will increase (decrease) surface pressure.

49. In class problems Group A Group B Scott Anna Alex James Justin Kevin
John
Ross
Rachel
Trent
Jordan

50. Initiation of flow
pressure surfaces
Earth’s surface

51. Introduction of warming
pressure surfaces
warming
Earth’s surface

52. Guiding questions pressure surfaces warming Earth’s surface
Questions for class
What happens to the pressure surfaces?
What happens to vertical velocity?
What happens to horizontal divergence?
What happens to the surface pressure?
What happens to the surface winds?
What happens to the wind at the top of figure?
warming
Earth’s surface

53. Take away points